$g(t) = -6t^{2}+f(t)$ $f(n) = -3n+6$ $ f(g(-2)) = {?} $
Solution: First, let's solve for the value of the inner function, $g(-2)$ . Then we'll know what to plug into the outer function. $g(-2) = -6(-2)^{2}+f(-2)$ To solve for the value of $g$ , we need to solve for the value of $f(-2)$ $f(-2) = (-3)(-2)+6$ $f(-2) = 12$ That means $g(-2) = -6(-2)^{2}+12$ $g(-2) = -12$ Now we know that $g(-2) = -12$ . Let's solve for $f(g(-2))$ , which is $f(-12)$ $f(-12) = (-3)(-12)+6$ $f(-12) = 42$